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By using the properties of definite int...

By using the properties of definite integrals, evaluate the integrals`int_0^pi (xdx)/(1+sinx)`

Text Solution

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Let `I=int_0^pi (xdx)/(1+sinx)`........(1)
`=>int_0^pi (pi-x)/(1+sin(pi-x))dx` `( int_0^af(x)dx=int_0^af(a-x)dx)`
`=int_0^pi (pi-x)/(1+sinx)dx`......(2)
Adding `(1)` and `(2)` we obtain
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